The curvy Brutalist-era complex was once the home of some of Britain’s favorite television series. Now it’s being turned into a high-end housing development, where prices start at $1 million.

For more than half a century, the BBC’s Television Centre in London produced some of Britain’s best-loved TV programs, from “Doctor Who” to “Monty Python’s Flying Circus” to “Absolutely Fabulous.”

The BBC left the site in 2013 to move to new studios, but work of another sort continues. Today, the curvy Brutalist-era concrete complex is being converted into a nearly $1.5 billion apartment development in the White City neighborhood of West London.

While the first phase of the project is scheduled for completion in 2018, sales officially launched last month. Prices start at $1 million for a one-bedroom, one-bathroom apartment measuring about 650 square feet. Two-bedroom, two-bath apartments (893 square feet) are priced at about $1.5 million, and the largest penthouses, priced at about $11 million, will have four bedrooms, four bathrooms and measure around 4,000 square feet.

So far, 240 of 432 units have been sold or reserved, several bought by people with connections to the BBC. “One chap who worked as a producer and now has his own very successful production company came back, worked out exactly where his old desk had been, and bought that apartment,” said Alistair Shaw, managing director of Television Centre, the company set up to oversee the redevelopment. The company is a consortium consisting of British developer Stanhope, Japan’s Mitsui Fudosan, and Canada’s Alberta Investment Management Corp.

On average, and excluding the penthouses, the price per square foot at Television Centre is $1,667. Mr. Shaw notes that for White City, these prices are high, but points out that people have been buying steadily for the past seven months. “We did wonder if we had actually underpriced it,” he said.

And White City, currently an ugly landscape of public housing, factory buildings and warehouses, crisscrossed by noisy railway lines and congested roads, is also the focus for major investment. Berkeley Homes is developing a site across the street from Television Centre with 1,500 new homes. The giant Westfield shopping mall is getting enlarged nearby, and Imperial College, one of Britain’s top science and technology universities, is building a research campus.

“White City is going to be a very different place in a few years’ time,” said Mr. Shaw.

Few commercial buildings hold such a strong place in British affections as Television Centre. “Everyone in the country has grown up looking at this building because of all the television shows that were filmed there, and because it was so often used as a backdrop for live broadcasts,” explained Paul Monaghan, a director at Allford Hall Monaghan Morris, the lead architect on Television Centre. “When people come in, they stop and take a selfie—there are not many buildings that have that effect.”

Affectionately called “the doughnut” because of its main, circular section, Television Centre in fact has a footprint more like a question mark. According to popular lore, the original architect, Graham Dawbarn, came up with the idea after doodling a question mark on the back of an envelope while designing the building, which opened in 1960.

The apartments are either within the doughnut or in a new arc-shaped building that will encircle it. The rest of the development will include 270,000 square feet of offices, restaurants, a movie theater and a new outpost of the Soho House hotel and members’ club. In all, the complex will measure close to 500,000 square feet.

The entire Television Centre site spans 14 acres, and in the second phase of this project—timing to be announced—will see another 500 apartments built, bringing the total cost of project Television Centre to $2.2 billion.

The main change to the building’s front facade is the color of its cladding, from blue to a deep, rusty red. The ugly parking lot in front of the building will be ripped out and landscaped with reading areas, a public-event space and gardens.

While efforts have been made to retain some of Television Centre’s original features, one beloved area has had to go. The “Blue Peter” garden, the backyard featured on a classic British children’s show that has been running since 1958, will be submerged beneath a restaurant terrace. The graves of generations of Blue Peter pets—the cats and dogs featured on the show—were carefully dug up and their remains relocated to the new BBC facility in Salford, in the north of England.

The apartments have been designed in a style that could be described as neutral with quirks. The walls are white, as are the kitchens, the floors are a midbrown oak, the windows are large.

But interior designer Suzy Hoodless has introduced some more unusual features, such as bathroom tiles based on a 1950s geometric design by Edith Heath, a celebrated American potter and ceramist.

She also sourced vintage furniture for the model unit to match the period of the building—which was completed in 1960—including a 1950s Danish sideboard and Eames DSW chairs.

Bespoke rugs, also in the model unit, have designs influenced by the architecture of the building, and artwork ranges from an original design for the 1908 Olympic Stadium (which was built near the site) to oil paintings. Communal hallways will be decorated with salvaged signs from Television Centre’s studios—one reads “Flashing Red Light Indicates Transmissions—Quiet Please.”

“I think that interiors have to look like they have been lived in over time, and not like you have bought a whole load of furniture all at once,” said Ms. Hoodless.

While the doughnut’s future as high-end housing is a very new role for Britain’s first purpose-built studio, it will still retain a small part in the television industry: The site also includes a studio that the BBC will continue to use. “It will not be a museum,” said Mr. Monaghan.